INTRODUCTION
IT was recognized first by Zehavi in [1] that a bit–interleaved coding scheme provides a diversity order for transmission over flat Rayleigh fading channels equal to the smallest number of distinct bits along any error event (rather than channel symbols). This scheme was later referred to as bit-interleaved coded modulation (BICM) in, where non–iterative decoding was considered and Gray labeling was thereby preferred. For frequency–selective fading channels, BICM schemes could also provide a high diversity order together with orthogonal frequency division multiplexing (OFDM) technique, where again Gray labeling is chosen for a non–iterative decoding strategy. However, Zehavi pointed out in his work that the non–iterative decoding method for BICM was not optimal, because the interdependence between labeling bits addressing one modulation symbol can not be exploited, since no a-priori information on the labeling bits is available. Therefore, for high order modulation with inevitable inter-dependence between the labeling bits, an optimal decoder exploiting this inter-dependence has a complicated metric.
On the other hand, a question naturally arises whether Gray labeling is still preferred if an enhanced decoding method is applied to take the inter-dependence between the labeling bits into account. By addressing the former problem of investigating an optimal decoder, a possible way is to consider the encoder, bit-interleaving and the mapper jointly with maximum likelihood (ML) decoding by means of a super-trellis diagram, but the trellis complexity may be extremely high in most cases with long interleaver. As an alternative, a suboptimal, iterative decoding method, which has been originally proposed for Turbo codes could be adapted in principle to BICM with necessary modifications to take advantage of the inter-dependence between coded bits by updating a-priori information on labeling bits. This has been originally introduced by Li and Ritcey in with a harddecision feedback method and the effects of different labeling strategies were discussed with the result that set partitioning (SP) rather than Gray labeling performs best. Furthermore, iterative decoding (ID) employing soft decision feedback, was applied to BICM (i.e., BICM-ID), too, yielding the result that when the inter–dependence introduced by high order modulation is somewhat exploited, a properly designed labeling rule different from Gray labeling will bring significant benefits.
Later on, this iterative decoding with bit interleaver was further adapted to multiple input and multiple output (MIMO) systems in several different approaches, and we preferred to denote this by bit interleaved coded space–time modulation with iterative decoding (BICSTM-ID) .since it closely resembles BICM in many aspects. As a natural consequence, designing a well suited labeling rule for space–time modulation (STM) is certainly essential as well. Therefore, one main aim of this paper is to analyze the performance of a bit-interleaved concatenated coding scheme over a MIMO channel with different labeling strategies, each of which is a component mapping composed of the space– time block code (STBC) and the labeling rule for a substitute constellation. For designing the labeling rules, some analytical methods for BICM-ID can serve as a good starting point such as the harmonic mean of the minimum squared distance d2 h in and modified one d2 h in by assuming ideal feedback information. The advantage of this modified parameter in is that an analytical bit error ratio (BER) upper bound for the nonlinear scheme can be provided.
However, in the low signal to noise ratio (SNR) region, this upper bound is not reliable and even lower than the simulation results due to the fact that in this region only part of ideal a-priori information may be actually fed back by iterative decoding. Moreover, it suffersfrom its inability to predict the cliff region.
IT was recognized first by Zehavi in [1] that a bit–interleaved coding scheme provides a diversity order for transmission over flat Rayleigh fading channels equal to the smallest number of distinct bits along any error event (rather than channel symbols). This scheme was later referred to as bit-interleaved coded modulation (BICM) in, where non–iterative decoding was considered and Gray labeling was thereby preferred. For frequency–selective fading channels, BICM schemes could also provide a high diversity order together with orthogonal frequency division multiplexing (OFDM) technique, where again Gray labeling is chosen for a non–iterative decoding strategy. However, Zehavi pointed out in his work that the non–iterative decoding method for BICM was not optimal, because the interdependence between labeling bits addressing one modulation symbol can not be exploited, since no a-priori information on the labeling bits is available. Therefore, for high order modulation with inevitable inter-dependence between the labeling bits, an optimal decoder exploiting this inter-dependence has a complicated metric.
On the other hand, a question naturally arises whether Gray labeling is still preferred if an enhanced decoding method is applied to take the inter-dependence between the labeling bits into account. By addressing the former problem of investigating an optimal decoder, a possible way is to consider the encoder, bit-interleaving and the mapper jointly with maximum likelihood (ML) decoding by means of a super-trellis diagram, but the trellis complexity may be extremely high in most cases with long interleaver. As an alternative, a suboptimal, iterative decoding method, which has been originally proposed for Turbo codes could be adapted in principle to BICM with necessary modifications to take advantage of the inter-dependence between coded bits by updating a-priori information on labeling bits. This has been originally introduced by Li and Ritcey in with a harddecision feedback method and the effects of different labeling strategies were discussed with the result that set partitioning (SP) rather than Gray labeling performs best. Furthermore, iterative decoding (ID) employing soft decision feedback, was applied to BICM (i.e., BICM-ID), too, yielding the result that when the inter–dependence introduced by high order modulation is somewhat exploited, a properly designed labeling rule different from Gray labeling will bring significant benefits.
Later on, this iterative decoding with bit interleaver was further adapted to multiple input and multiple output (MIMO) systems in several different approaches, and we preferred to denote this by bit interleaved coded space–time modulation with iterative decoding (BICSTM-ID) .since it closely resembles BICM in many aspects. As a natural consequence, designing a well suited labeling rule for space–time modulation (STM) is certainly essential as well. Therefore, one main aim of this paper is to analyze the performance of a bit-interleaved concatenated coding scheme over a MIMO channel with different labeling strategies, each of which is a component mapping composed of the space– time block code (STBC) and the labeling rule for a substitute constellation. For designing the labeling rules, some analytical methods for BICM-ID can serve as a good starting point such as the harmonic mean of the minimum squared distance d2 h in and modified one d2 h in by assuming ideal feedback information. The advantage of this modified parameter in is that an analytical bit error ratio (BER) upper bound for the nonlinear scheme can be provided.
However, in the low signal to noise ratio (SNR) region, this upper bound is not reliable and even lower than the simulation results due to the fact that in this region only part of ideal a-priori information may be actually fed back by iterative decoding. Moreover, it suffersfrom its inability to predict the cliff region.
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